153=16t^2+3t

Solution for 153=16t^2+3t equation:

153=16t^2+3t

We move all terms to the left:

153-(16t^2+3t)=0

We get rid of parentheses

-16t^2-3t+153=0

a = -16; b = -3; c = +153;
Δ = b2-4ac
Δ = -32-4·(-16)·153
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-99}{2*-16}=\frac{-96}{-32}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+99}{2*-16}=\frac{102}{-32}
=-3+3/16
$